The Secant Conjecture in the real Schubert calculus
Algebraic Geometry
2012-01-25 v3
Abstract
We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data.
Cite
@article{arxiv.1010.0665,
title = {The Secant Conjecture in the real Schubert calculus},
author = {Luis Garcia-Puente and Nickolas Hein and Christopher J. Hillar and Abraham Martin del Campo and James Ruffo and Frank Sottile and Zach Teitler},
journal= {arXiv preprint arXiv:1010.0665},
year = {2012}
}
Comments
19 pages